A wire carries a current of 0.71 A. This wire makes an angle of 46° with respect to a magnetic field of magnitude 6.4 × 10-5 T. The wire experiences a magnetic force of magnitude 8.9 × 10-5 N. What is the length of the wire?

2.72 m.

Explanation:

Using,

F = BiLsin∅ Equation 1

Where F = Force on conductor carrying current in a magnetic field, B = magnetic Field, i = current, L = Length, ∅ = angle between the wire and the magnetic field.

make L the subject of the equation

L = F/Bisin∅ Equation 2

Given: F = 8.9×10⁻⁵ N, B = 6.4×10⁻⁵ T, i = 0.71 A, ∅ = 46°

Substitute into equation 2

L = 8.9×10⁻⁵ /[6.4×10⁻⁵× 0.71×sin46°]

L = 8.9/[6.4×0.71×0.72]

L = 8.9/3.272

L = 2.72 m.

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we have been given a quadratic function and we need to restrict the domain such that it becomes a one to one function.

we know that vertex of this quadratic function occurs at (5,2).

further, we know that range of this function is .

if we restrict the domain of this function to either or , it will become one to one function.

let us know find its inverse.

upon interchanging x and y, we get:

let us now solve this function for y.

hence, the inverse function would be if we restrict the domain of original function to and the inverse function would be if we restrict the domain to .